This article gives a survey of recent research related to the Monge-Kantorovich problem.
Principle results are presented on the existence of solutions and their properties both in the …

Diffusion models are a powerful method for generating approximate samples from high-
dimensional data distributions. Several recent results have provided polynomial bounds on …

Abstract We study the Unadjusted Langevin Algorithm (ULA) for sampling from a probability
distribution $\nu= e^{-f} $ on $\R^ n $. We prove a convergence guarantee in Kullback …

We consider two related tasks:(a) estimating a parameterisation of a given Gibbs state and
expectation values of Lipschitz observables on this state;(b) learning the expectation values …

This textbook originated from the teaching experience of the first author at the Scuola
Normale Superiore, where a course on optimal transport and its applications has been given …

This is the first comprehensive introduction to the theory of mass transportation with its many—
and sometimes unexpected—applications. In a novel approach to the subject, the book both …

At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and
John Mather launched a revolution in the venerable field of optimal transport founded by G …

Concentration inequalities deal with deviations of functions of independent random
variables from their expectation. In the last decade new tools have been introduced making …

This book is concerned with the study of the probabilities of very rare events. To understand
why rare events are important at all, one only has to think of a lottery to be convinced that …

Includes material for a standard graduate class, advanced material not covered by the
standard course but necessary in order to read research literature in the area, and extensive …